{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# 第 6 节　正态分布及其应用\n",
    "## 第 3 章　使用 Python 进行数据分析｜用 Python 动手学统计学"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 1. 导入函数库"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "# 用于数值计算的库\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "# 用于绘图的库\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "sns.set()\n",
    "\n",
    "# 设置浮点数打印精度\n",
    "%precision 3\n",
    "# 在 Jupyter Notebook 里显示图形\n",
    "%matplotlib inline"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.338672Z",
     "end_time": "2024-04-16T17:24:18.348493Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 2. 实现：概率密度"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "data": {
      "text/plain": "3.142"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 圆周率\n",
    "np.pi"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.350494Z",
     "end_time": "2024-04-16T17:24:18.356202Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "2.718"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 指数函数\n",
    "np.exp(1)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.358195Z",
     "end_time": "2024-04-16T17:24:18.363195Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "0.228"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 均值为 4 标准差为 0.8 的正态分布在随机变量为 3 时的概率密度\n",
    "x = 3\n",
    "mu = 4\n",
    "sigma = 0.8\n",
    "\n",
    "1 / (np.sqrt(2 * np.pi * sigma ** 2)) * \\\n",
    "np.exp(- ((x - mu) ** 2) / (2 * sigma ** 2))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.362195Z",
     "end_time": "2024-04-16T17:24:18.370162Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "0.228"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.pdf(loc=4, scale=0.8, x=3)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.371163Z",
     "end_time": "2024-04-16T17:24:18.376394Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "0.228"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_dist = stats.norm(loc=4, scale=0.8)\n",
    "norm_dist.pdf(x=3)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.376394Z",
     "end_time": "2024-04-16T17:24:18.451336Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1521d5b8a10>]"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_plot = np.arange(start=1, stop=7.1, step=0.1)\n",
    "plt.plot(x_plot, stats.norm.pdf(x=x_plot, loc=4, scale=0.8), color='black')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.384311Z",
     "end_time": "2024-04-16T17:24:18.553553Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3. 样本小于等于某值的比例"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "array([5.299, 3.511, 3.577, ..., 4.065, 4.275, 3.402])"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "simulated_sample = stats.norm.rvs(\n",
    "    loc=4, scale=0.8, size=100000)\n",
    "simulated_sample"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.554553Z",
     "end_time": "2024-04-16T17:24:18.561569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "10371"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(simulated_sample <= 3)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.561569Z",
     "end_time": "2024-04-16T17:24:18.568723Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "data": {
      "text/plain": "0.104"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(simulated_sample <= 3) / len(simulated_sample)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.569726Z",
     "end_time": "2024-04-16T17:24:18.575913Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 5. 实现：累积分布函数"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "0.106"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(loc=4, scale=0.8, x=3)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.576914Z",
     "end_time": "2024-04-16T17:24:18.580401Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "0.500"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(loc=4, scale=0.8, x=4)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.582402Z",
     "end_time": "2024-04-16T17:24:18.635593Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 7. 实现：百分位数"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "data": {
      "text/plain": "2.432"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(loc=4, scale=0.8, q=0.025)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.589461Z",
     "end_time": "2024-04-16T17:24:18.635593Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "3.000"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left = stats.norm.cdf(loc=4, scale=0.8, x=3)\n",
    "stats.norm.ppf(loc=4, scale=0.8, q=left)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.595659Z",
     "end_time": "2024-04-16T17:24:18.635593Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "4.000"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(loc=4, scale=0.8, q=0.5)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.601902Z",
     "end_time": "2024-04-16T17:24:18.636595Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 10. t 值的样本分布"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [],
   "source": [
    "# 随机数种子\n",
    "np.random.seed(1)\n",
    "# 存放 t 值的空间\n",
    "t_value_array = np.zeros(10000)\n",
    "# 实例化一个正态分布\n",
    "norm_dist = stats.norm(loc=4, scale=0.8)\n",
    "# 开始实验\n",
    "for i in range(0, 10000):\n",
    "    sample = norm_dist.rvs(size=10)\n",
    "    sample_mean = np.mean(sample)\n",
    "    sample_std = np.std(sample, ddof=1)\n",
    "    sample_se = sample_std / np.sqrt(len(sample))\n",
    "    t_value_array[i] = (sample_mean - 4) / sample_se"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:18.606589Z",
     "end_time": "2024-04-16T17:24:19.323538Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\AppData\\Local\\Temp\\ipykernel_15912\\54034480.py:2: UserWarning: \n",
      "\n",
      "`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
      "\n",
      "Please adapt your code to use either `displot` (a figure-level function with\n",
      "similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "\n",
      "For a guide to updating your code to use the new functions, please see\n",
      "https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
      "\n",
      "  sns.distplot(t_value_array, color='black')\n"
     ]
    },
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1521d66d950>]"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# t 值的直方图\n",
    "sns.distplot(t_value_array, color='black')\n",
    "\n",
    "# 标准正态分布的概率祺\n",
    "x = np.arange(start=-8, stop=8.1, step=0.1)\n",
    "plt.plot(x, stats.norm.pdf(x=x), color='black', linestyle='dotted')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:19.323538Z",
     "end_time": "2024-04-16T17:24:19.611407Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 12. 实现：t 分布"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1521d5f4fd0>]"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, stats.norm.pdf(x=x), color='black', linestyle='dotted')\n",
    "plt.plot(x, stats.t.pdf(x=x, df=9), color='black')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:19.616403Z",
     "end_time": "2024-04-16T17:24:19.801265Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\AppData\\Local\\Temp\\ipykernel_15912\\1678669540.py:1: UserWarning: \n",
      "\n",
      "`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
      "\n",
      "Please adapt your code to use either `displot` (a figure-level function with\n",
      "similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "\n",
      "For a guide to updating your code to use the new functions, please see\n",
      "https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
      "\n",
      "  sns.distplot(t_value_array, color='black', norm_hist=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1521d710490>]"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(t_value_array, color='black', norm_hist=True)\n",
    "plt.plot(x, stats.t.pdf(x=x, df=9), color='black', linestyle='dotted')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:19.795253Z",
     "end_time": "2024-04-16T17:24:20.083855Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-16T17:24:20.084359Z",
     "end_time": "2024-04-16T17:24:20.086368Z"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
